scholarly journals STOCHASTIC MODEL FOR TIME TO RECRUITMENT IN A SINGLE GRADE MANPOWER SYSTEM WITH TWO TYPES OF INTERDECISION TIMES WHEN THE BREAKDOWN THRESHOLD HAS THREE COMPONENTS

YMER Digital ◽  
2021 ◽  
Vol 20 (11) ◽  
pp. 230-237
Author(s):  
A DEVI ◽  
◽  
K SRINIVASAN ◽  
Keyword(s):  
Stochastic Model ◽  
Renewal Process ◽  
Random Variables ◽  
Policy Decisions ◽  
Breakdown Threshold ◽  
Problem Of Time ◽  
Exponential Random Variables ◽  
Manpower System ◽  
System Characteristics ◽  
Three Components

In this paper, the problem of time to recruitment is analyzed for a single grade manpower system in which attrition takes place due to two types of policy decisions where this classification is done according to intensity of attrition, it form an ordinary renewal process. Assuming (i) policy decisions and exits occur at different epochs (ii) wastage of manpower due to exits and wastage due to frequent breaks taken by the personnel working in the manpower system separately form a sequence of independent and identically distributed exponential random variables with different means and (iii) breakdown threshold for the cumulative wastage of manpower in the system has three components which are independent exponential random variables. A stochastic model is constructed and the variance of the time to recruitment is obtained using an univariate CUM policy of recruitment. Employing a different probabilistic analysis, analytical results in closed form for system characteristics are derived.

scholarly journals DETERMINATION OF VARIANCE OF TIME TO RECRUITMENT WITH INTER-DECISION TIME AS GEOMETRIC PROCESS WHEN THE THRESHOLD HAS THREE COMPONENTS

YMER Digital ◽  
2021 ◽  
Vol 20 (11) ◽  
pp. 222-229
Author(s):  
A DEVI ◽  
◽  
B SATHISH KUMAR ◽  
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Decision Time ◽  
Breakdown Threshold ◽  
Geometric Process ◽  
Exponential Random Variables ◽  
Manpower System ◽  
Three Components ◽  
Independent And Identically Distributed

In this paper, the problem of time to recruitment is analyzed for a single grade manpower system using an univariate CUM policy of recruitment. Assuming policy decisions and exits occur at different epochs, wastage of manpower due to exits form a sequence of independent and identically distributed exponential random variables, the inter-decision times form a geometric process and inter-exist time form an independent and identically distributed random variable. The breakdown threshold for the cumulative wastage of manpower in the system has three components which are independent exponential random variables. Employing a different probabilistic analysis, analytical results in closed form for system characteristics are derived

scholarly journals Time to Recruitment for a Two Grade Manpower System by Max Policy of Recruitment

2018 ◽  
Vol 7 (4.10) ◽  
pp. 755
Author(s):  
K. Parameswari ◽  
P. Rajadurai ◽  
S. Venkatesh
Keyword(s):  
Policy Decisions ◽  
Manpower System ◽  
Mean And Variance ◽  
System Characteristics

In this paper an organization with two different grades, the grade wise depletion of manpower occurs due to its policy decisions is considered. Using max policy of recruitment the system characteristics namely mean and variance of time to recruitment are obtained by considering two different forms of wastages. The influence of the nodal parameters on the system characteristics is studied. 

On some characterizations of the poisson process

1989 ◽  
Vol 26 (01) ◽  
pp. 176-181
Author(s):  
Wen-Jang Huang
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Arrival Time ◽  
Random Variables ◽  
Poisson Processes

In this article we give some characterizations of Poisson processes, the model which we consider is inspired by Kimeldorf and Thall (1983) and we generalize the results of Chandramohan and Liang (1985). More precisely, we consider an arbitrarily delayed renewal process, at each arrival time we allow the number of arrivals to be i.i.d. random variables, also the mass of each unit atom can be split into k new atoms with the ith new atom assigned to the process Di, i = 1, ···, k. We shall show that the existence of a pair of uncorrelated processes Di, Dj, i ≠ j, implies the renewal process is Poisson. Some other related characterization results are also obtained.

scholarly journals Distribution of Minimal Path Lengths when Edge Lengths are Independent Heterogeneous Exponential Random Variables

2012 ◽  
Vol 49 (3) ◽  
pp. 895-900
Author(s):  
Sheldon M. Ross
Keyword(s):  
Joint Distribution ◽  
Shortest Paths ◽  
Random Variables ◽  
Simulated Data ◽  
Minimal Path ◽  
Exponential Random Variables ◽  
Path Lengths

We find the joint distribution of the lengths of the shortest paths from a specified node to all other nodes in a network in which the edge lengths are assumed to be independent heterogeneous exponential random variables. We also give an efficient way to simulate these lengths that requires only one generated exponential per node, as well as efficient procedures to use the simulated data to estimate quantities of the joint distribution.

Marshall–Olkin distributions, subordinators, efficient simulation, and applications to credit risk

2017 ◽  
Vol 49 (2) ◽  
pp. 481-514 ◽  
Author(s):  
Yunpeng Sun ◽  
Rafael Mendoza-Arriaga ◽  
Vadim Linetsky
Keyword(s):  
Credit Risk ◽  
Random Variables ◽  
Exponential Distributions ◽  
Efficient Simulation ◽  
Failure Times ◽  
Independent Unit ◽  
Exponential Random Variables ◽  
Credit Portfolio ◽  
Multivariate Exponential ◽  
Passage Times

Abstract In the paper we present a novel construction of Marshall–Olkin (MO) multivariate exponential distributions of failure times as distributions of the first-passage times of the coordinates of multidimensional Lévy subordinator processes above independent unit-mean exponential random variables. A time-inhomogeneous version is also given that replaces Lévy subordinators with additive subordinators. An attractive feature of MO distributions for applications, such as to portfolio credit risk, is its singular component that yields positive probabilities of simultaneous defaults of multiple obligors, capturing the default clustering phenomenon. The drawback of the original MO fatal shock construction of MO distributions is that it requires one to simulate 2n-1 independent exponential random variables. In practice, the dimensionality is typically on the order of hundreds or thousands of obligors in a large credit portfolio, rendering the MO fatal shock construction infeasible to simulate. The subordinator construction reduces the problem of simulating a rich subclass of MO distributions to simulating an n-dimensional subordinator. When one works with the class of subordinators constructed from independent one-dimensional subordinators with known transition distributions, such as gamma and inverse Gaussian, or their Sato versions in the additive case, the simulation effort is linear in n. To illustrate, we present a simulation of 100,000 samples of a credit portfolio with 1,000 obligors that takes less than 18 seconds on a PC.

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